MathDB

6

Part of 2012 ISI Entrance Examination

Problems(1)

square has maximum area... isi 2012 #6

Source:

5/13/2012
i) Let 0<a<b0<a<b.Prove that amongst all triangles having base aa and perimeter a+ba+b the triangle having two sides(other than the base) equal to b2\frac {b}{2} has the maximum area.
ii)Using i)i) or otherwise, prove that amongst all quadrilateral having give perimeter the square has the maximum area.
geometryperimetercalculusconicsellipseinequalitiesperpendicular bisector